Mean is the average value of set of numbers. Usually the term mean is referred arithmetic mean but there are different types of mean are there in math. Different types of mean are
arithmetic mean, arithmetic harmonic mean, geometric mean, geometric **harmonic mean**.

**Formula:**

**Arithmetic mean Formula** = `(a_1 + a_2 + a_3 +... + a_n) /
n`

Geometric mean Formula = `root(n)(a_1*a_2*a_3...a_n) `

`Where 'n' is the total number of elements in set. In this lesson we will discuss about how to find the arithmetic and geometric mean.`

**Example 1:** Find the arithmetic mean for following ages of 10 persons; 14, 15, 26, 31, 8, 2, 25, 42, 56, 72.

**Solution:**

Formula for find arithmetic mean is `(a_1 + a_2 + a_3 +... + a_n) / n`

Here a_{1} = 14, a_{2} = 15… and a_{10} = 72, n = 10

= `(14 + 15 + 26 + 31 + 8 + 2 + 25 + 42 + 56 + 72) / 10`

= `291 / 10` = 29.1

Therefore arithmetic mean of 10 person's age is 29.1.

**Example 2:** Find the arithmetic mean for following marks of 10 students; 52, 64, 72, 85, 98, 100, 15, 36, 50, 60.

**Solution:**

Formula for find arithmetic mean is `(a_1 + a_2 + a_3 +... + a_n) / n`

Here a_{1} = 52, a_{2} = 64… and a_{10} = 60, n = 10

= `(52 + 64 + 72 + 85 + 98 + 100 + 15 + 36 + 50 + 60) / 10`

= `632 / 10` = 63.2

Therefore arithmetic mean of 8 student's mark is 63.2

**Example 3:** Find the geometric mean for following heights of 8 students; 115, 171, 125, 156, 145, 156, 152, 167.

**Solution:**

Formula: Geometric mean =`root(n)(a_1*a_2*a_3...a_n) `

Here n = 8, a_{1} = 115, a_{2} = 171...a_{8} = 167

= `root(8)(115 * 171 * 125 * 156 * 145 * 156 * 152 * 167) = 147.17`

Therefore geometric mean of 8 student's height is 147.17.

**Example 4:** Find the geometric mean for following marks of 9 students; 25, 36, 25, 50, 62, 75, 81, 93 and 27.

**Solution:**

Formula: Geometric mean =`root(n)(a_1*a_2*a_3...a_n) `

Here n = 9, a_{1} = 25, a_{2} = 36...a_{9} = 27

= `root(9)(25 * 36 * 25 * 50 * 62 * 75 * 81 * 93 * 27) = 46.73`

Therefore geometric mean of 9 student's marks is 46.73.

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**Problem 1:** Find the arithmetic mean for following ages of 10 persons; 24, 25, 36, 41, 18, 12, 35, 52, 76, 92.

**Problem 2:** Find the arithmetic mean for following marks of 10 students; 42, 54, 73, 95, 58, 10, 18, 46, 60, 68.

**Problem**** 3:** Find the geometric mean for following heights of 8 students; 125, 151, 165, 146, 125, 176, 182,
197.

**Problem**** 4:** Find the geometric mean for following marks of 9 students; 35, 38, 35, 60, 72, 85, 51, 94 and 28.

**Answer: 1) **41.1** 2) **52.4** 3) **156.43** 4) **50.90